Foundations of Logical Consequence

Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.

1 - Logical Consequence: Its nature, structure, and application
2 - What is Logical Validity?
3 - Logical Consequence and Natural Language
4 - Is the Ternary R Depraved?
5 - Proof-Theoretic Validity
6 - The Categoricity of Logic
7 - The Meaning of Logical Terms
8 - Breaking the Chains: Following-from and Transitivity
9 - Non-Detachable Validity and Deflationism
10 - Embedding Denial
11 - Assertion, Denial, Accepting, Rejecting, Symmetry & Paradox
12 - Knowability Remixed
13 - Accuracy, Logic and Degree of Belief

Colin R. Caret is Assistant Professor of Philosophy in Underwood International College, Yonsei University, South Korea. Caret earned his PhD from the University of Connecticut and held a previous appointment as a Research Fellow in the Arché Research Centre (University of St Andrews). ; Ole T. Hjortland is Associate Professor of Philosophy at the University of Bergen, Norway. Hjortland has a PhD from the University of St Andrews. He has worked as a Research Fellow in the Arché Research Centre (University of St Andrews) and as Assistant Professor at the Munich Center for Mathematical Philosophy (LMU).